New machine learning application platform for spatial–temporal thermal error prediction and control with STFGCN for ball screw system

The big data platform, which has a high control accuracy and efficiency, is expected to realize the high-accuracy prediction and real-time control of the thermal error (TE) for the ball screw system. But the TE of a ball screw system has significant dynamic spatial–temporal behaviors. The TE model, which fully captures its dynamic spatial–temporal behaviors, has not been reported so far. Moreover, the embedding of the TE model into the big data platform is extremely difficult, and the deployment of the big data platform is time-consuming and relies on the expert knowledge, and the cloud computing used in the big data platform also faces a limited bandwidth pressure of the industrial Internet, leading to the failure of the real-time control. To overcome the above limitations, a novel machine learning application platform (MLAP) is designed based on the cloud-terminal architecture. Moreover, the spatial–temporal fusion graph convolutional network (STFGCN) is proposed for the first time to fully capture of the dynamic spatial–temporal behaviors, and the proposed STFGCN is embedded into the designed MLAP to expedite the training process of the STFGCN model and reduce the bandwidth pressure on the industrial Internet. The prediction performance and robustness of the proposed STFGCN model are compared with that of the traditional multiple linear regression (MLR), long short-term memory (LSTM), gated recurrent unit (GRU), convolutional neural network-long short-term memory (CNN-LSTM), temporal-graph convolutional network (T-GCN), hypergraph neural network (HGNN), spatial–temporal graph convolutional network (STGCN), and attention-based spatial–temporal graph convolutional network (ASTGCN). The results suggest that the evaluation metrics R2 of the MLR, LSTM, GRU, CNN-LSTM, T-GCN, HGNN, STGCN, ASTGCN, and STFGCN are 0.8039, 0.9500, 0.9441, 0.9414, 0.9571, 0.9512, 0.9689, 0.9712, and 0.9812 to show the prediction performance, respectively. Moreover, the training rate is improved by adding the number of the virtual machine nodes on the MLAP. The reduction rate of the machining error is the ratio of the machining error reduction to the original machining error. The positioning error and its fluctuation range of the ball screw system are reduced effectively, and the machining errors with the implementation of the MLAP are decreased by more than 33% and 72% compared with that with the pitch error control and without the TE control, respectively.